If you have players with expiring contracts. Do you have time after the season is over before they hit the FA pool like the NFL does, or do you have to resign them before the prior season ends?

You have to offer them a contract BEFORE season end, there is no buffer.

That really doesn't make any sense. You are being forced to get next years contracts on this seasons cap. NFL gives you till the first week in March to sign players whose contracts ran out.

Yep I agree.
Noobs often ask "If I offer a new 1 year contract, will it be for this season or next?.." The 1 year contract only applies to that current season, so even if you offer that player a contract a day before season end roll-over it will apply as a year contract then end the next day.
I believe that if you let their contract roll until the season end roll-over (ie, they'll be FA the next day) your offer will not be exclusive.

+1 i agree it would add an extra day but i think there should be a sim between end of season and 1st week of Early FA so you can sign your players that are about to go FA on the next years cap, just had to fight to keep a couple of my players because i was only 500k away from cap at end of season so i couldn't resign them until 1st week of Early FA which caused me to have to pay way more in cap for them than i would have if i'd been able to offer them exclusive contracts

Or just allow the option to offer a 6 year extension on a 1 year contract instead of the current season taking up the first year of the offer.

problem with that is you would still have to have the cap room to make the 1 year offer before end of season sim